It doesn't matter in what order the lists appear in, and it doesn't matter if they are separated by $k$, i.e., this function could give the lists of indices for a given $k$ value, or list all lists for $k=1 \dotsc n$ (the 14 in the example) in arbitrary order.

Yes, Subsets works perfectly here, thanks. Unfortunately I was looking for something that works for larger $n$, for example Subsets[100] exceeds machine integer size. You can do something like ask only for the $m$th subset of a particular size, but this is very slow. There may not be a feasible solution for large $n$.
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JohnApr 23 '14 at 21:52

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